Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#62050 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#529 ◁ G | |
1790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(9,12)(10,14)(16,17,21,26)(18,28,31,23)(19,32,34,41)(20,27,22,25)(24,36,39,33)(29,43,45,47)(30,38,35,40)(37,46,42,44);(8,9)(10,13)(11,12)(14,15)(16,18)(17,23)(19,29)(20,35)(21,31)(22,30)(24,37)(25,40)(26,28)(27,38)(32,47)(33,46)(34,45)(36,44)(39,42)(41,43);(16,19,21,34)(17,24,26,39)(18,29,31,45)(20,33,22,36)(23,37,28,42)(25,32,27,41)(30,44,35,46)(38,43,40,47);(9,12)(13,15)(16,20,21,22)(17,25,26,27)(18,30,31,35)(19,33,34,36)(23,38,28,40)(24,32,39,41)(29,44,45,46)(37,43,42,47);(8,10,11,14)(9,13,12,15)(17,26)(18,31)(24,39)(25,27)(29,45)(30,35)(32,41)(44,46)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55038);